This PDF is a selection from an out-of-print volume from the NationalBureau of Economic Research

Volume Title: The Behavior of Income Shares: Selected Theoretical andEmpirical Issues

Volume Author/Editor: Conference on Research in Income and Wealth

Volume Publisher: Princeton University Press

Volume URL: http://www.nber.org/books/unkn64-1

Publication Date: 1964

Chapter Title: A Survey of Some Theories of Income Distribution

Chapter Author: Tibor Scitovsky

Chapter URL: http://www.nber.org/chapters/c1842

Chapter pages in book: (p. 15 - 51)

A Survey of Some Theories of Income DistributionTIBOR SCITOVSKY

UNIVERSITY OF CALIFORNIA AT BERKELEY

THE theory of income distribution is in a highly unsatisfactoryand controversial state. Further thinking on the subject canbe facilitated by a survey that does the tedious but necessarypreliminary work of reviewing the field, putting it into somekind of order, and pointing out the more obvious strengths andflaws, connections and inconsistencies. It is in this spirit that thefollowing comments are offered.

There are at least four possible subjects that a theory of incomedistribution could cover: first, the level and changes in the levelof incomes earned in particular occupations; second, the distribu-tion and changes in the distribution of personal incomes by size;third, the functional distribution of income among the ownersof the different productive factors; and fourth, the relative sizeand changes in the relative size of the various components of theofficial personal income accounts.

The first, being the least ambitious, is probably also the mostpromising, but so little work has been done in this area thatthere is virtually nothing to review. On the second subject, themost important work, Champernowne's,' is beyond my grasp,and apart from that very little has been done. The availabledata cover too short a period of time to base theories on, and wehave not yet progressed beyond the simple notions of the classicaleconomists who looked to death duties and increasing educationto diminish inequalities of income. The effectiveness of thislast factor has recently been questioned,2 but there is still plentyof scope for more work on this subject. Another equally obviousinfluence on income distribution by size has never been men-tioned and may well be worth looking into. There is evidenceof a secular trend toward increasing centralization and an in-creasingly large-scale organization of economic, social, and politicallife; this means a changing pattern of demand for people, withfewer positions available in the higher and more in the lowerechelons. The demand for skilled people has declined relative

1D. G. Champernowne, "The Graduation of Income Distributions," Econo-October 1952, and "A Model of Income Distribution," Economic

Journcil, June 1953.2 H. P. Miller, "Income in Relation to Education," American Economic Re-

view, December 1960.

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SOME THEORIES OF INCOME DISTRIBUTIONto that for the unskilled, as has the demand for executives rela-tive to that for clerks and for generals relative to privates.Automation may well arrest or reverse this trend in the future,but in the past such changes in the pattern of demand may wellhave exerted on income distribution an equalizing force no lessimportant than the influences exerted on the supply side. Therising interest in the economic returns to education, viewed asinvestment in human resources, is likely to stimulate work on thisaspect of income distribution; but so far there is little or nothingto report on.

'Whereas on the first two subjects there has been too littletheorizing, on the third—the functional distribution of income—there are a large number of theories, using a variety of approachesand explaining a variety of phenomena; and hence it is in thisarea that there is the greatest scope as well as the greatest needfor a survey. Almost all of this work is concerned withthe twofold division between the share of labor in national incomeand the share of all other factors, loosely called capital. Theclassical system of three factors of production has been abandoned,largely because such categories as rent, interest, and profit inthe national income accounts bear little relation and cannot easilybe made to bear a meaningful relation to the factors land andcapital. This is also the reason why the fourth subject—distribu-tion by components of the national income accounts—has receivedlittle attention and tends to merge with the third subject.

The numerous theories of the division of income between laborand capital can be classified according to their approach and ac-cording to what they are trying to explain. As to the former,the distributive shares depend partly on the behavior of individualdecision-makers, entrepreneurs, and consumers, and partly onthe magnitude and pattern of demand and the relative supplyof the different factors. The theories that center attentionon the individual decision-maker's behavior are known as micro-economic theories; those that explain shifts in the distributiveshares by changes in demand, supply, or institutional factors weshall call macroeconomic explanations. Those that treat demandand the supplies of factors as endogenous variables, both deter-mined by and determining the distributive shares, we propose tocall macroeconomic theories.

As to the second method of classification, we shall distinguish16

SOME THEORIES OF INCOME DISTRIBUTIONbetween theories that explain the constancy and those that accountfor changes in the share of labor in national income. This,obviously, is not an exhaustive classification, but it covers mosttheories and all those we propose to deal with. Our discussionbegins with the second group of theories, all of which happento be macroeconomic explanations.

Short-Run Macroeconomic ExplanationsThe U.S. data show a pronounced anticyclical movement in labor'sshare of national income according to almost any of the customaryU.S. definitions of labor's share—i.e., wages and salaries, employeecompensation, or this plus some part of the earnings of the self-employed.3 The U.K. data show less regularity, primarily, I be-lieve, because labor's share traditionally means wages only; andwhereas the share of wages in wages and profits moves against thecycle, the share in total income (which also comprises salaries,rent, and interest) of wages and profits combined moves with thecycle, and these two contrary tendencies are mutually offsetting intheir influence on the share of wages in national income.4

The main explanation of the anticyclical behavior of labor'sshare (according to the U.S. definition) is, I believe, what Burk-head calls the capacity effect.5 The greater the utilization ofcapacity, the larger the output over which fixed costs are spreadand the smaller therefore the fixed costs per unit of output. Theimportance of this effect is probably increasing with the secularlyincreasing share of fixed in total costs and of supervisory and ad-ministrative workers in the total labor force.6

A second explanation of this anticyclical behavior is what somewriters call the lag i.e., the alleged lag of wages behindprice increases in times of prosperity and inflationary pressures.

a James C. Beck, "Labor's Share and the Degree of Utilization of Capacity,"Southern Economic Journal, April 1956; Jesse Burkhead, "Changes in the Func-tional Distribution of Income," Journal of the American Statistical Association,June 1953; Edward F. Denison, "Distribution of National Income since 1929,"Survey of Current Business, June 1952; Joseph Phillips, "Labor's Share and 'WageParity,'" Review of Economics and Statistics, May 1960.

4E. FT. Phelps Brown and P. E. Hart, "The Share of Wages in National In-come," Economic Journal, June 1952, pp. 253—277.

Burkhead, JASA, June 1953, p. 209.U Charles Schukze, Recent Inflation in the United States, Chap. 4, Study

Paper No. 1, Joint Economic Committee, 86th Congress, 2nd Session, Washington,1959.

Burkhead, JASA, June 1953, pp. 209—210.

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SOME THEORIES OF INCOME DISTRIBUTIONThat such a lag exists has for a long time been assumed by mosteconomists, on the basis partly of a priori reasoning and partlyof the evidence of the more spectacular hyperinflations of history.8All the recent evidence, however, seems to go counter to this notionand to show that prolonged inflation other than hyperinflationdoes not diminish labor's share in the national income, exceptin some cases of repressed inflation.9 This need not imply thata wage lag and consequent income redistribution cannot anddo not exist in the short run, at the peak of cyclical prosperity,during temporary bottlenecks and inflationary pressures. Thissubject, however, needs further investigation and one must keepan open mind in the interim.

A third explanation given by Burkhead is the compoundingthe cyclical shift to profits is also a shift to saving, and

the capitalists' higher savings give rise to higher incomes. I findthis explanation unconvincing, since the earnings of capital movepresumably with the stock of capital rather than its rate ofaccumulation.

A fourth explanation, which seems rather obvious but is notmentioned anywhere, might have to do with the composition ofoutput. Cyclical fluctuations in demand and hence output arefluctuations not only in magnitude but also in composition. Intimes of prosperity, demand and output are not only higher butalso different in composition, with investment goods and con-sumer durables and luxuries accounting for a larger share ofthe total. If labor's share in the income generated by these in-dustries is different from what it is in the rest of the economy,then their increased importance will also lead to a redistributionof income.11

We must also mention here the so-called Keynesian theoryS C. Bresciani-Turroni, The Economics of Inflation, London, 1937, especially

Chap. 8.° G. L. Bach and A. Ando, "The Redistributional Effects of Inflation," Re-

view of Economics and Statistics, February 1957; Economic Survey of Europe in1956, Geneva, United Nations, 1957, Chaps. 8 and 9; E. H. Phelps Brown andM. F!. Browne, "Distribution and Productivity under Inflation, 1947—57," Eco-nomic Journal, December 1960.

10Burkhead, JASA, June 1953, PP. 209—2 10.This factor, however, may well pull in the opposite direction. A rough

calculation based on recent U.S. data shows that in investment goods industries(construction and producer durables) the share of employee compensation intotal income generated was 75 per cent, higher than the 69 per cent averagefor the economy as a whole. The inclusion of consumer durables and luxuries islikely to diminish the disparity but not to reverse it.

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SOME THEORIES OF INCOME DISTRIBUTIONof distribution, the rudiments of which are contained in theTreatise on Money and which has been further developed byBoulding, Hahn, Kaldor, Kalecki, and Robinson.12 This is animplicit theory, which links investment and income distributionby analyzing the latter's effect on the community's propensityto save, postulating the equality of saving and investment as anequilibrium condition, and tacitly taking for granted that a risein investment will somehow redistribute income in favor ofcapital. It has been criticized, even ridiculed, for taking forgranted what a proper theory of income distribution ought toexplain explicitly;13 it may be fairer, however, and more fruitfulto inquire into the causal factors that it takes for granted. Thetheory is supposed to apply equally to underemployment andfull-employment situations (though Kaldor and Robinson wouldrestrict it to the latter); at least as far as the former are concerned,the U.S. data certainly bear out the theory, and the macro-economic explanations just discussed can serve as the causal factorsimplicit in it. If labor's share in national income is inverselycorrelated with the level of national income within the businesscycle, it must be similarly correlated—and for the same reasons—with the share of net investment in net national income, which weknow to be directly correlated with the level of income. Onethinks first of the capacity effect as the most obvious reason whya rise in investment should, through its stimulating effect on thelevel of income and capacity utilization, reduce the relative shareof labor; and the lag effect seems a possible further explanationtoo.

As to the validity of the theory in full-employment situations,I know of no statistical evidence; but if the capacity effect and thelag effect adequately explain a fall in labor's share during cyclicalupswings of falling unemployment, they should also explain afall in labor's share resulting from rising investment at timeswhen the labor force is fully employed. This is certainly sowhen a rise in investment at a time of full employment implies

13K. E. Boulding, A Reconstruction of Economics, New York, 1950, Chap. 14;F. Hahn, "The Share of Wages in the National Income," Oxford EconomicPapers, June 1951; N. Kaldor, "Alternative Theories of Distribution," Reviewof Economic Studies, No. 61, 1955—56; M. Kalecki, "A Theory of Profits," Eco-nomic Journal, June-September, 1942, pp. 258—261; J. Robinson, The Accumulationof Capital, London, 1956.

iaj• Tobin, "Towards a General Kaldorian Theory of Distribution," Review ofEconomics Statistics, February 1960.

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SOME THEORIES OF INCOME DISTRIBUTIONan increase in hours worked and an expansion of the labor force.The argument becomes more complex when the rise in investmentinvolves a transfer of resources from other sectors of the economy;but the capacity effect and the lag effect are operative and mayexert the dominant influence even then. Some adherents of theKeynesian theory seem aware of its limitations (Robinson's "infla-tion barrier" and Kaldor's "subsistence minimum" indicate somedistrust of the lag effect), and within such limits its validity shouldnot be denied merely because one is annoyed by the way inwhich it is stated.

Long-Run Macroeconomic ExplanationsIn addition to countercyclical changes, the U.S. data also showa secular increase in labor's share of the national income; allthe economists who have worked with these data have soughtand found special explanations to account for this trend.14 Oneof these is the increasing importance of the government contri-bution to the national product, since, according to present ac-counting practice, this consists solely of employee compensa-tion. Another explanation is the secularly diminishing impor-tance of agriculture, where labor's share in value added is especiallylow and where, in addition, labor's real income is understated inview of the lower-than-average prices paid by farm workers. Athird explanation is the secularly rising proportion of wage andsalary earners and the diminishing proportion of small (i.e.,unincorporated) businessmen in the total labor force.

It is to isolate and eliminate the effect of this last factor thatit has become customary in the United States to define the laborshare or service share as employee compensation plus all or partof the earnings of unincorporated business, regarded as "entre-preneurial labor income."5 The effect of the diminishing im-portance of agriculture is isolated by comparing the actual shareof labor to what it would be if the weights of the differentsectors had remained constant;1° the effect of government's in-

14Denison, Survey of Current Business, June 1952; Phillips, RES, May 1960;Dale H. Johnson, "The Functional Distribution of Income in the United States,1850—1952," Review of Economics and Statistics, May 1954, Pp. 175—182; 1. B.Kravis, "Relative Income Shares in Fact and Theory," American Economic Re-view, December 1959, pp. 917—949.

15Johnson, RES,, May 1954; Kravis, AER, December 1959; Burkhead, JASA,June 1953; Edward C. Budd, "Factor Shares, 1850—1910," in Trends in theAmerican Economy in the Nineteenth Century, Studies in Income and Wealth,24, Princeton for NBER, 1960.

leJohnson, RES, May 1954, p. 180; Kravis, AER, December 1959, pp. 934—935.

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SOME THEORIES OF INCOME DISTRIBUTIONcreasing importance is eliminated by excluding the governmentcontribution from both national income and labor's share.17

There are a number of other factors as well, such as the in-fluence of war and the great depression on the decade estimatesand the change in the source and nature of the data at the verydate (1929) when they seem to show the greatest change in labor'sshare. lATe shall pay no more attention to these factors, however,because the first three explanations between them deal, to thesatisfaction of most writers on the subject, with just about all thesecular change in labor's share of the national income in theUnited States.'8

These conclusions are at least as interesting for what they implyas for what they actually say. Economists who try to explainchanges in distributive shares by invoking special factors and par-ticular trends seem to believe in the constancy of distributiveshares, which would obtain if it were not for these special factors.And if they succeed in explaining fully the changes in relativefactor shares by these special factors, then they have come closeto proving indirectly the existence of other factors at work whichtend to maintain the stability of distributive shares. Further sup-port for this line of reasoning comes from a comparison of theAmerican and the British data. The latter show that the share inthe national income of wages alone was virtually constant overthe period 1870—1950, with swings no greater than 8 per centaway from the average.19 When one recalls that in Britain agricul-ture was much less important throughout this period, and that theother two factors—the increasing importance of government andthe rising proportion of employees—both affect salaries and notwages, then the British findings appear to confirm rather than tocontradict the U.S. data; and they strengthen the feeling that theremust be other factors making for the constancy of distributiveshares.2° Some people may also wish to attach importance to thefact that all the factors invoked to explain the secular change in

Denison, Survey of Current Business, June 1952; Phillips, RES, May 1960,pp. 177 if.; Kravis, AER, December 1959, p. 927; George J. Schuller, "The SecularTrend in Income Distribution by Type, 1869—1948: A Preliminary Estimate,"Review of Economics and Statistics, November 1953; Johnson, RES, May 1954,pp.

Kravis alone feels differently and, for an earlier period, Budd. Unfortunately,the latter's paper reached me too late for more than a cursory glance.

Phelps Brown and Hart, Economic Journal, June 1952.It is worth noting in this connection that Budd, dealing with U.S. data for

1850—1910, finds a greater stability in the share of wages than in that of wagesand salaries or of services.

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SOME THEORIES OF INCOME DISTRIBUTIONdistributive shares in the United States are macroeconomic. Whilethis proves nothing, it might rule out some macroeconomic expla-nations of constancy and suggest that we should at least begin oursearch for the explanation of the constancy of distributive sharesamong the microeconomic factors.

Micro economic TheoriesThe first of these is the marginal productivity theory of distribu-tion. It is worth recalling that parts of this theory were, to someextent, originally developed to provide a rebuttal of Marx's theoryof exploitation and an ethical basis for the distribution of incomein a free enterprise economy. This explains the argument, on theassumption of perfect competition, that each factor's rate of re-muneration equals the value of its marginal contribution to output,and the related argument, based on the assumption of long-runcompetitive equilibrium, that the capitalist gains nothing frombeing in the seemingly advantageous bargaining position of theentrepreneur who does the hiring and firing.2'

Today, we no longer seek ethical content in economic theories,and many of us have become reluctant to assume perfect compe-tition and long-run equilibrium; nevertheless, most people stilladhere to the marginal productivity theory. For one thing, itsgenerality and elegance has considerable appeal; for another, it fitsin best with our marginalist approach to economics; for a third,the acceptance of the marginal productivity theory of income dis-tribution is closely bound up with the assumption of an aggregateproduction function whose analytic convenience has enticed manyeconomists to slur over or disregard the objections to it. Its mod-ern form, however, is a very much watered-down version of theneoclassical marginal productivity theory and amounts to littlemore than a market theory of income distribution. By this wemean a theory that stresses merely that the rates of remunerationof productive factors are market prices determined by supply anddemand, and influencing in turn the quantities and proportionsin which individual entrepreneurs demand the services of the pro-ductive factors.

The main purpose to which the theory is put nowadays is toexplain the relative stability of factor shares. Given a market the-

I am here referring, of course, to the use of Euler's theorem for solving theadding-up problem.

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SOME THEORIES OF INCOME DISTRIBUTIONory of income distribution, it is enough for demand curves toslope downward and for the main disturbances to come from thesupply side in order to assure contrary and hence offsetting move-ments in factor supplies and factor prices. These, in turn, assurethe relative stability of factor shares, in the sense that factor sharesin total income fluctuate relatively less than either factor suppliesor factor prices. That such stability exists becomes obvious on con-sidering that the supply of reproducible capital has increased twiceas fast as the supply of labor;22 and there is no need at this stageto enter the controversy over how constant something must beto be called constant. Those who believe in the constancy of rela-tive factor shares have further assumed unit or near-unit elasticityof substitution between labor and capital, and also neutral techni-cal progress—this latter to explain the constancy of shares even inthe face of some disturbances (technical progress) coming fromthe demand side. These assumptions, however, are not an integralpart of the marginal productivity or market theory of incomedistribution and may be left aside while we analyze the theory.

The theory that rates of factor remuneration are and behavelike market prices implies the assertions, first, that the quantitiesand proportions in which the services of the productive factorsare demanded depend on relative prices; and second, that totaldemand for productive services influences their prices. We pro-.pose to offer some critical comments on both these assertions.

As to the first, factor substitution in response to a change inrelative factor prices can be direct and indirect. Direct substi-tution is made by entrepreneurs; and it is well known, thoughnot stressed often enough, that the scope for this is extremelylimited. The proportions in which the entrepreneur combineslabor and capital in his day-to-day production decisions are largelydetermined by the nature of his productive equipment and meth-ods, which have been fixed for the useful lifetime of his plant atthe time when he built his factory and bought his equipment.Changing relative prices influence the entrepreneur's factor pro-portions mainly through their impact on his investment decisions;and these affect factor proportions only in a small fraction of thetotal productive system.23 The manufacturing capacity created

Kravis, AER, December 1959, p. 918.The fact that disused capacity can be brought back into production does

not really modify this statement. For the change in factor proportions that23

SOME THEORIES OF INCOME DISTRIBUTIONby gross investment in the average year is only about one-tenthof total manufacturing capacity.

It is also worth asking exactly how a change in prices influencesthe proportions in which labor and capital are combined in invest-ment projects. The standard argument is that a rise in wagesrelative to product prices will lower the profitability of investmenton all investment projects, but to a lesser extent on the morecapital-intensive ones, which is why demand will shift towardcapital. The tacit assumption underlying the argument is that thetotal volume of investment remains unchanged despite the reducedprofitability of all investment (and despite the higher wage level,which may affect total consumption), and that total income andemployment also remain unchanged. When this assumption isfalse, the effects of changed levels of investment and income onthe nature of investment and on income distribution must also betaken into account; and these effects may modify or change theargument. Because the scope for direct factor substitution byentrepreneurs is so limited, economists have stressed the impor-tance of indirect factor substitution by consumers. A rise in therelative price of labor raises the prices of labor-intensive goodsrelative to those of capital-intensive goods; this prompts consumersto shift their demand from the former to the latter, thereby in-directly bringing about a shift in demand from labor to capital.The argument is impeccable, but its importance must be judgedby empirical results. For indirect factor substitution by consum-ers, in contrast to direct factor substitution by entrepreneurs,exerts its influence on factor shares through interindustry shifts,and these should be separable from the forces that operate withinan industry. Suggestive in this connection is Solow's finding thatinterindustry and intersector shifts in demand and output have hadno stabilizing effect on labor's share in aggregate income;24 but it

this implies is usually incidental and comes about in response to a rise in de-mand, whichever way relative factor prices have shifted. With demand un-changed, relative factor prices would have to change drastically indeed to bringdisused capacity back into use.

Robert M. Solow, "A Skeptical Note on the Constancy of Relative Shares,"American Economic Review, September 1958, pp. 618—631. Solow presents hisfindings as an argument against relying on macroeconomic explanations of thestability of factor shares. I am not familiar, however, with any macroeconomictheory that would invoke interindustry shifts as a stabilizing factor, except for theargument of this paragraph, which is an integral part of the marginal produc-tivity or market theory of income distribution.

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SOME THEORIES OF INCOME DISTRIBUTIONis only suggestive, partly because his data relate to industries andsectors too broadly defined to have too much bearing on the pres-ent argument, and partly also because his conclusions, even ifbased on a finer industry classification, would prove the unim-portance of indirect factor substitution by consumers only in the(to my mind likely) case that the elasticity of direct and indirectsubstitution combined should be nearer unity than the elasticity ofdirect substitution alone.25

We can now proceed to examine the second assertion, which isthat the change in factor proportions wrought by individualdecision-makers in response to a change in relative prices willchange total market demand for the different factors and thus in-fluence, in its turn, relative factor prices. Two observationsneed to be made in this connection. One is that this part of themechanism will operate only at high activity levels, for it isdifficult to imagine the forces of demand and supply in factormarkets influencing prices at times when the labor force, existingplant capacity, and the potential supply of savings are all under-utilized.

Our other observation is that to analyze the effectiveness ofthis part of the mechanism would require a detailed comparativestudy of price and wage behavior both between the capital goodsand other sectors and between periods when plant capacity ismore fully utilized than the labor force and periods when thereverse is true. Some such studies are being made as part of thecurrent analysis of inflation, an important by-product of whichmay well be additional information on and insight into the work-ings of factor markets.

To sum up, our criticism of the market theory of income dis-tribution is that it is based too little on direct evidence abouthow factor markets operate and too much on analogy with the verymuch simpler operation of market supply and demand and substitu-tion in markets for consumer goods. We do not deny that marketforces operate in factor markets; but they may be much weakerand much more sluggish than is generally supposed; and for all weknow they may, in some respects, operate quite differently fromthose that operate in the market for bread.

At best the market theory explains not constancy but merelyI am indebted to Professor M. Reder for cautioning me against reading too

much into Solow's elegant argument.

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SOME THEORIES OF INCOME DISTRIBUTIONa fair degree of stability in factor shares, and even that only in theface of disturbances coming from the supply side. To explainthe constancy of relative factor shares would require unit elas-ticity of factor substitution. There is quite a literature, to whichwe can only refer here, to warn against accepting unit elasticityon the evidence that the Cobb-Douglas function gives a good fitto time-series data.26 On the other hand, several people havepointed out recently that what constancy there is in relative fac-tor shares in the United States is compatible not only with unitelasticity but also with a whole range of values of the elasticity ofsubstitution if this is not too far removed from unity, and es-pecially if it is above unity.27 The first reaction to this argumentis to point out that the elasticity of substitution would be expectedto be below rather than above unity,28 and to ask what is "nottoo far removed." W/e have neither statistical estimates of theelasticity of substitution nor intuition to tell us what are reasonableor likely values.

As to disturbances emanating from the demand side, the dis-cussion in the previous two sections has shown that factor sharesare affected by quite a variety of changes that emanate from thedemand side; there is only one such change, though a major one,that seems to have left relative shares unaffected—technologicalprogress. The kind of progress that leaves relative factor sharesunchanged has been defined as neutral; and the fact that progressin our economy has been so close to neutral needs an explanationand can hardly be regarded as an accident of history. No satis-factory explanation has been offered as yet by the upholders ofthe marginal productivity theory; some tentative explanationsoffered by others will be discussed in the next section.

A second microeconomic theory of income distribution isKalecki's theory.29 This is a first cousin of the marginal pro-

E. H. Phelps Brown, "The Meaning of the Fitted Cobb-Douglas Function,"Quarterly Journal of Economics, November 1957; and some of the literature re-ferred to there.

M. Bronfenbrenner, "A Note on Relative Shares and the Elasticity of Substi-tution," Journal of Political Economy, June 1960; also Solow, AER, September1958, P. 629; and Kravis, AER, December 1959, p. 940.

2S all, the relative supply of labor has been diminishing and its relativeshare has, if anything, increased.

M. Kalecki, "The Determinants of Distribution of the National Income,"Econometrica, April 1938, reprinted with significant changes in his Essays inthe Theory of Economic Fluctuations, London, 1939, and also in his Theoryof Economic Dynamics, London, 1954.

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SOME THEORIES OF iNCOME DISTRIBUTIONductivity theory, from which it differs, in a formal sense, bydropping the assumptions of perfect competition and long-runequilibrium, and making instead the simplifying assumption ofconstant returns to scale (horizontal marginal and average directcost curves)—at least within the range of underemployment, whichis Kalecki's sole concern. The main determinant of income dis-tribution in his theory is the percentage gross profit marginentrepreneurs add to marginal or average direct cost in settingtheir prices, and Kalecki regards this as an index of the degreeof monopoly. In early versions of his theory, this is determinedby (and stands in a definite relation to) the price elasticity ofdemand facing the entrepreneur; in the last version, the degree ofmonopoly is more generally defined in order to include oligopolyas well.

The great merit of Kalecki's theory is that it relates incomedistribution to the entrepreneur's pricing policy and makes thestability of distributive shares partl.y dependent on the stabilityof entrepreneurial profit margins. This means that it is a short-run theory, which has to do with the firm's day-to-day pricing de-cisions. Thus it contrasts with (and perhaps complements) themarket theory, which is a long-run theory and mainly has to dowith the entrepreneur's investment decisions and very little withhis day-to-day decisions on the relation of prices to wages and thedetermination of output in the face of given prices and wages.Kalecki's theory suffers from the lack of a satisfactory and inte-grated theory of monopolistic and oligopolistic competition; andit may well be that a fully satisfactory explanation of distributiveshares will have to await the development of such a theory. Hissimplifying assumption of horizontal marginal cost curves hasbeen justly criticized;30 but its abandonment only complicateswithout destroying his theory. It should also be stressed that thetheory explains distributive shares in the gross product, not innet income, and hence allows for cyclical fluctuations in theincome shares; that labor's share in the theory means the shareof wages only and excludes salaries that do not enter prime costs;and that vertical differentiation also plays an important role.Kalecki himself believes in a secular increase in the degree of con-centration and monopoly and provides a somewhat unconvincing

Melvin W. Reder, "Rehabilitation of Partial Equilibrium Theory," AmericanEconomic Review, May 1952, pp. 191—192.

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SOME THEORIES OF INCOME DISTRIBUTIONargument for reconciling this with the constancy of distributiveshares; but others, testing his model, have found the degree ofmonopoly to be constant.3' Further testing of his model shouldinvestigate the importance and implications of the alleged secularshift from wage-earning production workers to salaried super-visory and administrative employees. With Kalecki's theorylinking distributive shares to the firm's pricing policy and themarket theory linking it to the firm's investment decisions, oneshould hope that future work on the theory of investment by thefirm, and on the influence of the firm's monopoly power andpricing policy on its investment decisions, will provide the meansto integrate these two microeconomic theories of income distri-bution.

Macroeconomic TheoriesThe classical example of this group of theories is Ricardo'ssubsistence theory of wages. This asserts that the wage rate al-ways tends toward the subsistence level, because a higher wagewill raise the birth rate and a lower one will raise the death rateof workers, thereby increasing or diminishing the supply of laborand thus depressing or raising wages until they return to the sub-sistence level and equilibrium in the supply of labor is restored.

The beginnings of a modern macroeconomic theory of incomedistribution can be found in—or read into—Hicks' Theory ofWages, where he introduces the idea of induced technical changein an attempt to account for the stability of factor shares. Heknew that the market theory of distribution explains the relativestability of factor shares only in the face of disturbances emanatingfrom the supply side, and even then only when the elasticityof substitution is near unity. This accounts for his attempt tomake the nature of innovation depend on economic factors, but hisargument is hard to follow and incomplete. It is similar, however,to part of the theory to be discussed presently and will be re-ferred to below in that connection.

Another macroeconomic theory, and perhaps the most satis-factory one, can be pieced together from an article by E. H.Phelps Brown and B. Weber and from several papers by N.Kaldor.32 The first two authors have shown that in England not

Ashok Mitra, The Share of Wages in National income, The Hague, 1954.E. H. Phelps Brown and Bernard Weber, "Accumulation, Productivity and

Distribution in the British Economy, 1870—1938," Economic Journal, June 1953,

28

SOME THEORIES OF INCOME DISTRIBUTIONonly the share of capital in income but also the rate of return oncapital invested and the level of output per unit of capital have allshown a remarkable constancy over time. Any two of these im-ply a third, so that if the constancy of two is explained, the con-stancy of the third follows. Accordingly, Phelps Brown andWeber, in a tentative theoretical explanation of their findings, ar-gue the existence of economic forces that keep stable the first andthe third relations mentioned above. Kaldor, in his turn, explainsthe same findings in terms of economic forces stabilizing thefirst and second relations and obtains the stability of the thirdas a consequence. 'We shall argue presently that while neitherapproach is fully convincing, the two combined provide a bettertheory than either of them singly.

Phelps Brown and Weber explain the stability of the firstrelation—the share of capital in total income—by a propensityof businessmen to maintain, at least in the short run, a fixed pro-portional relation between prices and direct costs. In otherwords, they accept Kalecki's theory in its simplest form, findingstatistical confirmation of this constancy by Phelps Brown andHart.83 Kaldor relies on essentially the same argument, althoughhis explanation is very differently worded.

The existence of forces stabilizing the second relation—therate of return on capital invested—is developed in detail by Kaldoralong lines reminiscent of Ricardo's subsistence theory of wages.34He argues that the expected rate of earnings on capital must exceedthe market rate of interest by a minimum margin in order to repaythe entrepreneur for his risk and trouble; that when expectedmargins exceed this minimum, the resulting faster rate of capitalaccumulation will soon depress rates of return and bring expectedmargins closer to the minimum; whereas if expected margins fallbelow the minimum, the consequent choking off of capital ac-cumulation will soon raise the margin again if population continuesto grow and technology to progress. Kaldor's argument explains

pp. 263—288; N. Kaldor, "A Model of Economic Growth," Economic Journal,December 1957, pp. 591—624; Kaldor, "Economic Growth and the Problem ofInflation," Economica, August 1959, pp. 2 12—226 and 287—298; Kaldor, "CapitalAccumulation and Economic in The Theory of Capital, New York,1961.

83 Brown and Hart, Economic Journal, June 1952, pp. 267—268.Brown and Weber also mention this as a possibility but do not

elaborate it.

29

SOME THEORIES OF INCOME DISTRIBUTIONa long-run stability not so much of the rate of return on capitalas of the margin between this rate and the market rate of intereston riskless securities; but in view of the latter's historical be-havior, Kaldor's theorem fits Phelps Brown's data very well.It might be added that there is nothing marginal about Kaldor'sexpected future rate of profit on capital invested, since this isbased on the past actual rate of profit, which in turn is the ratioof profit per output (the net profit margin) to capital per output.

The long-run stability of the third relation, the capital-out-put ratio, is again argued by Phelps Brown and Weber, or ratherthey outline and refer to an argument found in more detail else-where. As is well known, when the return on capital is constant,a proportional rise in output and the stock of capital meansneutral technical progress. And neutral technical progress can beequated, as a rough first approximation, to parallel productivityincreases in consumer goods and capital goods industries; forproductivity increases in the former are labor-saving, those inthe latter capital-saving improvements. Phelps Brown and Weberexpect the neutrality of technical progress to be assured by theforces that tend to keep productivity increases in these twogroups of industries parallel. These forces have been better de-scribed in the literature on economic development, especially bythe critics of the doctrine of balanced growth.35 A productivityincrease in one industry generates pressures on other industriesto raise their productivity too. These pressures take a varietyof forms: the squeezing of profits in competing and the creationof bottlenecks in related and complementary industries. Anearlier generation of theorists would have concluded that a changein relative prices would lead to a gradual shrinking of the formerand expansion of the latter industries; but a closer look at the his-torical evidence (and perhaps also a new fashion in theorizing)suggests that this will only happen as a last resort. Establishedfirms will do their utmost to improve productivity and lowercosts before accepting the death sentence of dwindling profits;and bottlenecks are usually broken not by a gradual expansion ofthe factor in short supply but by a technical breakthrough thatdispenses with or greatly reduces the need for this factor. There

Albert 0. Hirschman, The Strategy of Economic Development, New Haven,1958, especially Chap. 4; also my "Growth—Balanced or Unbalanced?" in M.Abramovitz et al., The Allocation of Economic Resources, Stanford, 1959.

30

SOME THEORIES OF INCOME DISTRIBUTIONis mounting evidence that one innovation leads to another througheconomic pressure as much as through the similarity of technicalconditions and problems; and if all this leads to parallel increasesin labor productivity, it also assures neutral technical progress.Needless to say, this is no exact equilibrating mechanism but a veryrough and approximate equalizing force.

As already mentioned, Phelps Brown and Weber rely on thislast and on the first equilibrating force to account for the sta-bility of the three relations; Kaldor relies on the first two anddeduces the neutrality of technical progress as an indirect conse-quence.36 There is no need, however, to choose between thesetwo explanations. If any two of the three equilibrating forceswere strong, the third would indeed be unnecessary for explain-ing the stability of the three relations; but this is not the case.Parallel increases of productivity in different industries are atbest a very long-run and approximate tendency; and equallylong run is the tendency of capital accumulation to influence theprofitability of capital. By contrast, the entrepreneur's tend-ency to maintain a stable relation between prices and directcosts is a short-run stabilizing influence, which may be subjectto secular change. The three stabilizing forces therefore shouldbe recognized as mutually reinforcing, and the theories of Kaldorand Phelps Brown and Weber as complementary. They need tobe developed further and restated more carefully but are never-theless the most, perhaps the only, satisfactory macroeconomictheory of income distribution. It should be noted in closing thatthis theory does not hinge on interindustry shifts, is therefore notsubject to Solow's criticism,37 and can accommodate the changesin income distribution brought about by interindustry shifts, whichare discussed among the macroeconomic explanations.

COMMENTEDWARD F. DENISON, Brookings Institute

Professor Scitovsky provides a short survey of distributiontheories that I found useful, enlightening, thought-provoking, and,

most nearly complete and satisfactory statement of Kaldor's theory iscontained in the unpublished paper mentioned in footnote 32. His presentationis more suggestive and persuasive than this account, owing primarily to the useof his "investment function" as an explanatory device.

Cf. footnote 24.

31

SOME THEORIES OF INCOME DISTRIBUTIONhappily, presented without a single mathematical symbol. For thisI salute him.

Insofar as Scitovsky is simply reporting the views of others,he must, in all fairness, be considered immune to criticism. How-ever, he also classifies the various theories, and points out their mostimportant strengths and flaws, connections and inconsistencies.Here he is fair game and if we can use the pretext of his commentsto strike a blow at any of the authors he cites, so much the better.In the latter part of my comment I shall attempt to do so.

Scitovsky devotes almost all of his paper to the functionaldistribution of income. However, he gives only the barest mentionto the distribution of national income by type of income, as pub-lished by the Commerce Department. This series reports the formin which income initially accrues to suppliers of the factors of pro-duction, before government steps in to take and give via taxes andtransfer payments. This is one of the most interesting distribu-tions, and not only because we have some data that we can try toexplain. It is, after all, the distribution that most of the shoutingis about. The public outcry is not over the functional distributionas economists define it but about how the income of farm propri-etors is too low, or corporate profits have been squeezed, or aretoo big, and so on. Work by Charles Schultze, among others, hasshown how illuminating analysis based on this classification can bein examining business fluctuations. I suspect it would also be use-ful to try to bring the tools of economic theory and empirical in-vestigation to bear upon the reasons that this distribution is what itis, and has changed as it has over longer periods. Those who thinkthe division of income between corporations and persons has some-thing to do with the saving rate, and this includes most economists,should be interested in such a study. Some work has been donefor individual shares, such as the income of farm proprietors andindependent professionals, but not, I think, comprehensively.Any general theory would have to include both the determinantsof the various legal forms of organization and the compositionof the resources going into the mixed shares in terms of the classi-fications used in economic theory.

The theories that Scitovsky does discuss, insofar as they relyon data at all, reverse this process. Instead of trying to develop atheory to explain the data, they try to adjust the data to a classi-fication that theory can explain, or restrict themselves to only a

32

SOME THEORIES OF INCOME DISTRIBUTIONportion of the economy where statistics and the shares of theorycorrespond, or else slur over the differences. Only infrequentlydo they seriously try to go beyond a simple two-way division be-tween labor income and all other income.

For the study of such a classification, the economy can bebroken down into three parts. In one—private corporations or-ganized for profit—the actual shares correspond tolerably well tothose of theory. In a second part—proprietorships and partner-ships—any division of income into the categories of economictheory is simply a reflection of the assumption on which it is based.In the rest of the economy—government, households and institu-tions, noncorporate ownership of real property, erc.—each eco-nomic unit gives rise almost entirely to either labor or nonlabor in-come so that within it there is little problem of the distributionof income. But this does not mean these economic units can beignored, nor that theory can simply deal with the rest of theeconomy as if they didn't exist. In 1957 they contributed one-fifth of labor income. They contributed almost one-third of non-labor income if corporate profits are measured before tax and al-most one-half of nonlabor income if corporate profits are measuredafter tax,1 as would seem appropriate for those theories relying onthe rate of return or some relation between saving and after-taxlabor and nonlabor incomes. They absorb labor or capital, as thecase may be, and create income that is spent or saved. Most of thetheoretical models, as distinguished from the statistical studies, thatScitovsky discusses seem incapable of accommodating these entities.

Scitovsky's classification of theories by what they are tryingto explain seems to me inadvertently to bias and limit the subse-quent discussion in a way that is very much to the disadvantage ofthe marginal productivity theory. He says, "we shall distinguishbetween theories that explain the constancy and those that accountfor changes in the share of labor in national income." That is tosay, he deals with theories that will explain why, if labor income is70 per cent, it will remain at 70 per cent or will grow to 75 percent. But he does not consider why it was 70 per cent rather than10 or 100 per cent in the first place.

It does not seem to me that this question can be answered with-

1This calculation divides national income Originating in proprietorships andpartnerships between labor and property income in the same proportion as in-come originating in corporations.

33

SOME THEORIES OF INCOME DISTRIBUTIONout reference to marginal productivity. The marginal produc-tivity theory also purports to explain occupational differentials,which the other theories he discusses do not. The marginal pro-ductivity theory itself is consistent with any statistical division ofnational income between labor and other income, until the quan-tities, functions, etc., needed to arrive at some numerical divisionare introduced. Von Thünen was the first to try to take this the-ory as a point of departure to use observed data to derive a formulathat would yield a numerical answer for the statistical distributionof income. Acceptance of the marginal productivity theory didnot rest on the validity of von Thünen's formula, and I doubt thatit will or should rest on anyone else's formula. Scitovsky assertsthat the main purpose to which the theory is put nowadays is toexplain the relative stability of factor shares. But the theorycannot itself be tested by seeing whether or not the distributionis stable.

The exclusive focus on changes or stability in the labor shareof income, as distinct from its level, avoids any discussion ofwhether the macroeconomic theories Scitovsky describes can ex-plain, or even are consistent with, equilibrium for individual eco-nomic units. I wish Scitovsky had indicated, in each case, whetherthe theorist was trying to explain why economic forces, operatingthrough the marginal productivity process, lead to some particularchange or lack of change in the distribution of national income, orwhether he has some other concept of equilibrium or none at all.

I am particularly interested in the part of Scitovsky's pape.rwhere he pieces together what he calls "perhaps the most sat-isfactory macroeconomic theory." I shall try to show that it isnot satisfactory at all, and indeed is completely untenable for theUnited States from the late twenties to the present. In this sec-tion, if we follow Scitovsky, we need be concerned with onlythree numbers, although two more are hiding under the table:(1) nonlabor income, which sometimes gets called income fromcapital and which I shall therefore call C; (2) total national incomeor product, which I shall call Y; and (3) total capital input orcapital stock, which I shall call K. If we set down the ratio ofeach of these three numbers to the other two, we get three ratios,and any two ratios determine the third. WTe can write the ecjua-tion: C/V (the nonlabor share of national income) equals C/K(the rate of return on capital) times K/Y, the ratio of capital input

34

SOME THEORIES OF INCOME DISTRIBUTIONto national product. If two of these ratios happen to be constantover time, the constancy of the third follows automatically.Scitovsky notes that Phelps Brown and Weber argue that economicforces keep the nonlabor share of national income and the capital-output ratio constant, and this makes the rate of return constant.Kaldor thinks that economic forces keep the nonlabor share of na-tional income and the rate of return on capital constant, and thisexplains constancy in the capital-output ratio. Finally, Scitov-sky himself suggests that all three ratios have some tendency to-ward stability and these three stabilities mutually reinforce oneanother.

The important thing to note is that the equation holds only ifthe same numbers are used for nonlabor income, national income,and capital input each time they appear in the ratios. I concedethat, taking each ratio separately, there is some definition of thenumerator and denominator that will yield a ratio that evidencesno clear and pronounced upward or downward long-term trend.This is not a very stringent statistical test of stability, since anyseries that fluctuates at random will meet it, but I shall waive thequestion of what stability means. The point I wish to developis that there is no set of definitions which, if uniformly applied,will allow all three ratios to show long-term stability in the UnitedStates by even the loosest definition of stability. If this is so,the whole argument collapses.

Let me note first that, to use only three series and three ratios inthe equation, it is necessary to use prices of the same date in allthree ratios. Actually, it is customary to use current prices in thefirst two ratios and constant prices in the capital-output ratio. Infact, the theoretical rationale for stability in each requires thatthis be done. On this basis, balance requires that the right sideof the equation be multiplied by another ratio, that of capital stockprices to national product prices. Our theorists get around thisdifficulty by assuming that productivity increases at the same ratein the production of capital goods as in that of consumption goods,and hence that prices will increase at the same rate, so this ratiotoo is stable. But actually, the ratio of prices of capital goods out-put to other prices has risen hugely—by about one-third since1929, implying that productivity has increased vastly less in capitalgoods production than elsewhere. Maybe the price indexes are nogood and this did not really happen, but in the absence of alterna-

35

SOME THEORIES OF INCOME DISTRIBUTIONtive data there can be no empirical support for the assumption ofequal productivity and price changes in capital goods industriesand elsewhere. And these are the same price data used in meas-uring real capital stock.

Second, the ratios must refer to the same part of the economy—either all of it or some clearly defined sector. Most favorable tothe argument—since it is the only way a tolerably constant incomedistribution can be obtained—is to deal with corporations alone,or else with what I have called elsewhere the ordinary businesssector, consisting of corporations, proprietorships, and partner-ships. This is pretty awkward for the theoretical argument, as Ihave already suggested, but let us waive that too. For what Ireally want to stress is the definition of nonlabor income, C, andof capital input, K. Nonlabor income enters into two ratios. Itis absolutely necessary to include corporate income taxes to makenonlabor income a constant fraction of national income in corpo-rate or ordinary business. Even then the data for the last fewyears suggest a downward movement in the nonlabor share butlet us waive that.

But to get a stable rate of return on capital it is necessary, andthe theoretical argument seems to require, that corporate profitsbe measured after deduction of corporate income taxes. TheMachinery and Allied Products Institute (MAP!) estimates forcorporations make the point very clearly.2 With their adjust-ments, profits before tax averaged 19.2 per cent of corporate in-come produced in 1923—29 and 21.4 per cent from 1950 to 1959.Inclusion of interest would largely eliminate any change. Profitsafter tax dropped from 16.0 to 9.6 per cent of corporate .nationalincome, or by two-fifths, and inclusion of interest would furtheraccentuate the change. On the other hand, profits after tax were5.6 per cent of net worth from 1923 to 1929 and 5.5 per cent from1950 to 1959. But on a before-tax basis, the rate of return in-creased from 6.5 to 11.1 per cent, or by seven-tenths.3 Thisgeneral characteristic of the profits record is well known. It popsup particularly in discussions of the incidence of the corporation

2Data cited in the following paragraphs are those underlying charts presentedin the Capital Goods Review, May 1959.

8 Other estimates do not yield so clear-cut a result as the MAPI estimates.Comparison of Office of Business Economics profits estimates with RaymondW. Goldsmith's net stock figures suggest the before-tax rate of return has risenwhile the after-tax rate has fallen. On this basis, there is no stable ratio to beexplained.

36

SOME THEORIES OF INCOME DISTRIBUTIONincome tax. The stability of before-tax corporate income in thecorporate national income total suggests the tax is not shifted,while the stability of the rate of return computed after tax suggestsit is shifted.

For the first two ratios, C/Y and C/K, both to be constant whennonlabor income, C, is defined in the same way, total income, thedenominator of the first ratio, would have to rise by the sameamount as the net capital stock, the denominator of the secondratio. MAPI estimates show the ratio of income produced incorporations to corporate net worth increased from 27.2 per centin 1923—29 to 47.6 per cent in 1950—59, or by three-fourths.Under these conditions there cannot be any definition of nonlaboror property income that will yield stability in both the nonlaborshare of national income and the rate of return.

This brings me to the measure of capital, K, which appears inthe second and third ratios. In the second, the rate of returncalculation, the denominator is the net capital stock, and it mustbe the net capital stock if the ratio is to be stable statistically or ifthe theoretical argument for stability is to be sensible. But as wehave just seen, if the net capital stock is used in the third ratio, thecapital-output ratio, and it is computed in current dollars, thatratio drops drastically.

Even when we measure the capital-output ratio in constantprices, if we use the net capital stock to measure capital input theratio drops dramatically from the twenties to the recent period. Isupposed this to be well-known from the work of Kendrick,Kuznets, and Goldsmith, and surely so since Arthur Smithies'attempt to explain this change appeared in the Quarterly Journalof Economics last May.

The stable constant-dollar capital-output ratio can still be sal-vaged, or nearly so, if capital input is measured by constant-dollardepreciation on structures and equipment rather than by capitalstock. This works out with both the Kendrick and the MAPIestimates for, say, the years 1909, 1929, and 1957. A case can bemade that this is the way capital input of structures and equip-ment ought to be measured, and that the ratio of depreciation tonet output is the one that could be expected to be stable on apriori grounds. But if stability in the capital-output ratio isachieved by the use of depreciation to measure capital input, de-preciation would also have to be substituted for net stock in the

37

SOME THEORIES OF INCOME DISTRIBUTIONsecond ratio, and this would make the "rate of return" dropdrastically. Nor would there be any theoretical reason to expectstability.

I do not think that changes of two-fifths to seven-tenths in aratio meet even the most tolerant ideas of stability. They seemto me sufficient to dispose of any notion that stability in two ofthe ratios can explain stability in the third, or that, as Scitovskysuggests, stability in all three can be mutually reinforcing.

It is true, of course, that the English authors cited in this sectionhave relied on English as well as United States statistics. But onlythe article by Phelps Brown and Weber tries to deal simulta-neously with the three ratios. And they say that in the 1924—38period one of the ratios, that of capital to output, was about thesame as from 1870 to 1914, while the other two ratios were bothvery different. Within the 1924—38 period they find that the ratioof real output to real capital rises sharply, while the other tworatios are supposed not to have shown a trend, although this is notvery clear from their charts. Neither within nor between periodsis stability of all three ratios really claimed. The three ratios arenot given for individual years. Nor are any data subsequent to1938 provided.

One might suggest that the model builders, in particular, woulddo well to look a little more carefully at the numbers before theyset out to rationalize them. But even to the extent they do, itsometimes seems to matter but little. Thus Kaldor, in one of thearticles cited by Scitovsky, appends a footnote that Phelps Brèwnand Weber indicate a rising capital-output ratio in England from1900 to 1914 and a falling ratio for 1924—38, and that in theUnited States the ratio rose from the 1880's to 1909—18, ignoringthe depression period, has shown a falling trend since, and is notsignificantly different now from what it was sixty years ago. Inother words, I interject, the ratio has behaved in a perfectly randomfashion. But not to Kaldor. Returning to the text, he criticizesexisting theories because they cannot explain such constanciesexcept (and I quote) as the result of "some coincidence—as, e.g.,that 'capital saving' and 'labour saving' inventions happened (his-torically) to have precisely offset one another."4 In a similarvein, Scitovsky remarks in his present paper that the marginal

Nicholas Kaldor, "A Model of Economic Growth," Economic Journal, De-cember 1957, pp. 592—593 (my italics).

38

SOME THEORIES OF INCOME DISTRIBUTIONproductivity theory "at best explains not constancy but merely afair degree of stability in factor shares." One can only wonderhow any theory can be criticized on this ground!

FRANCO MODIGLIANI, Northwestern University1. Scitovsky's valuable and stimulating survey offers quite a

tempting range of topics to pick from for a discussant. But tokeep this comment within bearable limits, I shall have to confinemyself to a criticism of the last section of his survey, in which hereviews and elaborates upon various "macroeconomic theories"designed to provide an explanation for the "observed" long-runstability of the three ratios. These are: (1) the share of property(i.e., nonlabor) income P in total income Y, or P/Y; (2) the ratioof the stock of capital K to income, or capital coefficient, K/Y;(3) the rate of return on capital, r = P/K. As Scitovsky remindsus, these three ratios are not independent so that the constancy ofany two implies the constancy of the third.

I shall pass by the issue of whether the empirical evidenceadequately supports the long-run stability of these ratios. Forone thing, even if these ratios have not remained absolutely con-stant, it would seem at the very least that their long-run fluctua-tions have been quite moderate by comparison with the very largechanges which have occurred in each of the numerators and de-nominators separately, as well as in such ratios as output per em-ployed or capital per employed. Besides, the task of explainingthe stability is such a fascinating and challenging game that it ishard to resist, even if the stability is after all a figment of some-body's imagination!

My comments fall into two parts. First, I should like to offersome criticism of Scitovsky's largely favorable review of thetheories advanced by Kaldor and by Phelps Brown and Weber.I propose to argue that neither of these models, at least as inter-preted by Scitovsky, is satisfactory, and more specifically that thefirst, though logically correct, is unconvincing, while the secondis neither convincing nor logically correct. Having thus clearedthe ground of opponents, I shall proceed to summarize an alterna-tive explanation which has been advanced in some earlier workof mine, and which Scitovsky did not include in his survey.

2. Kaldor's theory, as interpreted by Scitovsky, is an exceed-ingly simple and ingenious one. Also, contrary to most other ex-

39

SOME THEORIES OF INCOME DISTRIBUTIONplanations, it succeeds in explaining the stability of the capital-output ratio with no explicit reference to, or reliance on, the natureof technological progress, or, for that matter, on marginal produc-tivity and the price mechanism. Stated very simply, it relies onthe identity between the ratio of capital to output and the ratioof the rate of return on sales to the rate of return on capital, or,

(P/Y)/(P/K), (1)

and on two mechanisms accounting respectively for the long-runstability of the numerator and the denominator ratio.

The stability of the numerator, according to Scitovsky, is ex-plained by the hypothesis that producers set prices by adding aconstant percentage mark-up, say, rn/ (1 — m) to unit labor cost.As is well known, such a constant mark-up policy implies thattotal labor cost, or labor income, will tend to represent a constantfraction (1 — rn) of total product F', and therefore the rate ofreturn on sales P/V will tend to be rn—a result of which Wein-traub1 has made a good deal.

This mechanism is supplemented by a second one whichScitovsky hardly discusses and which insures that the rate ofreturn on capital r will gravitate toward a long-run equilibriumvalue r, pulling in turn the capital output ratio toward an "equi-librium" value k = The essential ingredient of this mecha-nism is the hypothesis that the rate of investment depends both onthe rate of growth of income (the conventional accelerationprinciple) and on the rate of return on capital. The postulatedrelation is such that when r = f, and hence k = k, the rate ofgrowth of capital just equals the rate of growth of income, withthe result that K/Y stays put at and hence also r at —

If, however, at any point K/F' should happen to fall short of k,say, because of technical change or other disturbance, then as aresult of the unchanged mark-up rn, the rate of return on capitalwould rise above The increase in r in turn leads to a step-up inthe rate of investment, which causes capital to grow faster thanincome, so that K/V will rise back toward thereby also pullingr back toward r.

I should add at this point that my interpretation of Kaldor'smodel, based on his published work,2 is somewhat different in the

1S. Weintraub, A General Theory of the Price Level, Output, Income Dis-tribution and Economic Growth, Philadelphia, 1959.

'I am referring in particular to "A Model of Economic Growth," EconomicJournal, December 1957, pp. 591-624.

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SOME THEORIES OF INCOME DISTRIBUTIONdetails, if not in the broad outline. As I see it, the constancy ofthe capital-output ratio is based on the interaction of his investmentfunction with his "technical progress function" (stating that therate of change of output is a function of the lagged rate of growthof capital). These two functions insure that the rate of growthof both income and capital must gravitate toward an equilibriumrate G, and hence income and capital must tend to become pro-portional. Given this rate of growth, the share of property in-come P/Y and the capital coefficient are simultaneously determinedwith the help of the investment function and by relying onKaldor's peculiar theory of distribution, according to which thefactor shares are determined, of all things, by the ratio of invest-ment to income.

However, these differences of interpretation are perhaps a mat-ter of detail. \Vhat is essential is that, in either interpretation, thecornerstone of Kaldor's model is the assumption that, even at fullemployment, the rate of investment is completely determined bythe investment demand; whatever this demand, the level of savingand consumption passively adjusts to it through the intermediaryof Kaldor's amazing theory of distribution. Hence, even withoutcriticizing other aspects of his model, such as his nondescript "tech-nical progress function," anyone who, like myself, is inclined toshare Tobin's dim view of Kaldor's theory of distribution andsaving behavior must regard his whole explanation as uncon-vincing, in spite of its undeniable ingenuity.

3. The Phelps Brown and Weber model again accounts for thestability of the labor share in terms of a stable mark-up on laborcosts; but, in contrast to the Kaldor model, it endeavors to explaindirectly the stability of the capital coefficient—the stability of therate of return being thus accounted for as a necessary consequenceof the other two. Unfortunately, just how Phelps Brown andWeber propose to explain the stability of the capital coefficientis not very clear, either in their original work or in Scitovsky's in-terpretation. Scitovsky seems to suggest that this stability is de-rived from the constancy of the shares plus the hypothesis thattechnological change has been neutral on balance, which is itselfexplained by a variety of forces. There are unfortunately twoserious difficulties with the passage in which Scitovsky advancesthis proposition. In the first place, neutral technical change hasbeen defined in a variety of ways., and Scitovsky fails to makeclear which concept he is adopting, although from the context

41

SOME THEORIES OF INCOME DISTRIBUTIONone must conclude that he refers to Harrod's Second,and more important, it is in general not true that constancy of theshares and Harrod-neutral technical change imply constancy of thecapital-output ratio.

In order to establish this point, let us recall that Harrod's defini-tion can be paraphrased as follows: technical change between someinitial date 0 and some later date t is neutral if, the rate of interestbeing unchanged between the two dates, the most economical

Outputper employed

y

0

(least-cost) input combination implies an unchanged capital out-put ratio, i.e., if r0 = Tt implies = K0/Y0 (it being assumedthat the least-cost combination in fact prevails). It will be useful,for later reference, to exhibit analytically and graphically justwhat Harrod-neutral technical change implies with respect to theshift in time of the production function. Let Y F0 (K,E) denotethe production function (homogeneous of first degree) at theinitial date, E standing for total employment. Making use of thehomogeneity properties, it can be rewritten as: y f(k), wherey = Y/E and k = K/E denote respectively output per employedand capital per employed. This function can be represented bya curve in the (y,k) plane, such as the solid curve of Figure 1.

R. Harrod, Towards a Dynamic Economics, London, 1948, p. 23.

42

///fo

Capitol per employed

FIGURE 1.

SOME THEORIES OF INCOME DISTRIBUTIONIt should be noted that the slope f'0(k) of this curve for any givenvalue of k represents the marginal productivity of capital for thegiven input combinations, and therefore also the rate of interest forwhich k is the least-cost combination.

Now, let X = (K,E) denote the production function at datet. It can be readily established that if the shift in the productionbetween 0 and t is Harrod-neutral throughout, must be relatedto F0 by the equation

= F0[K,H(t)E] (2)

where H(t) > 1 if in fact technology has improved. In otherwords, for any given combination of inputs, the output with thenew production function will be the same as if the production func-tion had remained unchanged but labor input had been increased bya factor H(t), or each worker had become the equivalent of H(t)workers. Because of the homogeneity, the new production func-tion at time t can be restated in the form

Y/[H(t)EJ = f0[K/H(t)E], or y = ft(k) = H(t)f0{k/H(t)].(3)

In terms of Figure 1, the new production function ft is representedby a curve such as the dotted one, which can be derived from thefo curve as follows: through any point q of the old function, drawthe radius vector Oq and extend it to the point q', such thatOq'/Oq = H(t). Then q' is on ft, and ft itself is the locus ofsuch points obtained by sliding q along fo. To verify that thislocus represents a Harrod-neutral shift of the locus fo, we needonly to observe that, by construction, the slope of ft at q' is thesame as the slope of fo at q. In general, therefore, for any givenrate of interest or slope, the point chosen on ft and that chosenOn fo will lie on the same radius vector. But this in turn impliesthat these two points will be characterized by the same capitalcoefficient, since along any radius vector we have y/k =(Y/E)/(K/E) = V/K = constant. In fact, the slope of theradius vector through any point q, when referred to the y axis,represents precisely the capital coefficient at q. It should be notedthat the shift in the production function between 0 and t might beHarrod-neutral in a neighborhood without being so throughout.

We may add in passing that Harrod's definition of neutral change

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SOME THEORIES OF INCOME DISTRIBUTIONis quite different from the most common or "classical" one, ac-cording to which a change is neutral if, and only if, for every com-bination of inputs, the ratio of the marginal product of any two in-puts is the same for as for Fo; that is, the marginal productivityof all factors rises in the same proportion. This definition impliesthat, if the shift between 0 and t is classical-neutral, then isrelated to F0 by the equation (K,E) = C (t) F0 (K,E), withC(t) > 1. Similarly ft is related to fo by the relation x = ft(k) =C(t)f0 (k). Thus ft can be obtained graphically from fo by multi-plying the ordinate of each point on fo by the factor C (t).

Now it is immediately apparent from the definition and fromour graph that, if technical change is Harrod-neutral, constancyof the capital output ratio implies constancy of the shares. For, inthis case, we know we are moving from a point such as q on fo toa point q" on ft lying on the radius vector Oq, and since the slopesat q' and q are the same, we must have Tt = ro. But this condi-tion, together with the relation = K0/Yo, assumed ex hy-pothesis, implies = roKo/Yo, i.e., constancy of the shares.Unfortunately the converse proposition, on which Scitovsky seemsto rely, is not true: that is, constancy of the shares does not neces-sarily imply constancy of the capital-output ratio. The easiestway of disproving Scitovsky's inference is to provide a counter ex-ample. Suppose, then, that the production function F0 is of theCobb-Douglas variety, or, say, X = F0 (K,E) = Sup-pose next that is another Cobb-Douglas function of the form

Y = = = F0{K,H(t)E]= (4)

By comparing equation (4) with equation (2), we see that theshift from 0 to t satisfies the definition of Harrod-neutrality. Atthe same time, from a well-known property of the Cobb-Douglasfunction we know that, if factors are paid their marginal product,the share of capital is given by a, the exponent of K, independentlyof the input combination chosen. Since the exponent of K doesnot change between 0 and t, we must have roKo/Yo Po/Yo =a = i.e., the shares are constant. And yet from this infor-mation, we can make no inference whatever about the capital-output ratios which are respectively K0/Y0 = (1/A)and = (1/A) and will be equal if, and

44

SOME THEORIES OF INCOME DISTRIBUTIONonly if, Kt/Et = H(t) (K0/E0). In other words, at least in thisparticular example, the constancy of the shares, plus Harrod-neu-trality, does not entitle us to draw any conclusion about the be-havior of the capital-output ratio.

The shortcoming in Scitovsky's argument which we have justbrought out could no doubt be remedied by imposing some furtherspecifications on the nature of the production function and/ortechnical progress. But even if this were done, another and morefundamental flaw would remain in the proposed explanation ofthe constancies. To see that this must indeed be the case, we needonly observe that in the model under discussion we find no ref-erence, explicit or implicit, to the supply side of the capital market,i.e., to the set of forces or mechanisms controlling the community'swillingness to accumulate capital through the process of saving.This is an important departure from the Kaldor model, in which,at least, such a mechanism was provided for, even if not very con-vincingly. Surely there must be something wrong with a line ofreasoning that purports to draw conclusions about the stock ofcapital and its behavior in time merely from information abouttechnical knowledge and pricing behavior. Fortunately, the flawis not too difficult to ferret out: the root of the difficulty lies in anunholy marriage of a marginalistic model of factor remuneration,with a mark-up----and hence nonmarginalistic—model of price de-termination. To be more specific, in order to make inferencesabout factor shares from the hypothesis of Harrod-neutral tech-nical change, we must conceive of the capital share or rate of re-turn on sales P/V as determined by r and by the capital-laborratio chosen by producers in response to r, which in turn impliesa unique value for the capital-output ratio K/Y, and hence finallyfor rK/Y = P/V. But then we cannot simultaneously postulatethat P/V is determined independently by an exogenously given"customary" mark-up on labor costs. In brief, the explanationsused to establish the constancy of P/V and that of K/V are incon-sistent with each other!

4. Let me now move on to the more constructive task of outlin-ing an alternative model which can also account for the historicalconstancies and which, at the same time, meets Scitovsky's chal-lenge of accomplishing this task within the framework of the mar-ginal productivity approach. The argument developed belowis to some extent a summary of parts of a recent paper by Albert

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SOME THEORIES OF INCOME DISTRIBUTIONAndo and myself,4 although it places much greater stress on therole of technical progress (which was treated only in passing inour paper) and relies on less restrictive assumptions.

The point of departure of the model is a theory of saving behav-ior, the main elements of which were first presented in my jointpaper with R. Brumberg, "Utility Analysis and the ConsumptionFunction: An Interpretation of Cross-Section Data."5 As shownin the essay I wrote with Ando, cited above, and in otherthis model implies an aggregate consumption function of the form

+ where Ct denotes the current rate of consump-tion at time t and the (anticipated) rate of nonproperty in-come, both measured in terms of current prices, and repre-sents the aggregate current market value of households' net worth.It has also been shown that the coefficient c (a pure number) andb (with dimension 1/time) will tend to be roughly constant intime, at least as long as the rate of return on capital, r, and thegrowth trend of are roughly constant. For purposes of long-run analysis, which is our present concern, we can identifywith current labor income, to be denoted by Xt. In the interest ofbrevity, we may also ignore here the existence of nonreproducibletangible wealth and of government operations (including the na-tional debt). Under these conditions W can be identified with re-producible tangible wealth, or K, and private income, X + rKcoincides with net output, Y.7 The long-run aggregate consump-tion function thus becomes:

Ct — + = + rgKt)+ (b — rtc)Kt = cYt + (b — rtc)Kt. (5)

"Growth, Fluctuations and Stability," Americcm Economic Review, May1959, pp. 501—524.

In Post-Keynesian Economics, K. Kurihara, editor, New Brunswick, N.J.,1954.

0F. Modigliani and R. Brumberg, "Utility Analysis and the Aggregate Con-sumption Function," mimeographed; A. K. Ando, "A Contribution to the Theoryof Economic Fluctuations and Growth," Ph.D. thesis, Graduate School of In-dustrial Administration, Carnegie Institute of Technology, 1959; A. K. Andoand F. Modigliani, "The 'Life Cycle' Hypothesis of Saving: Aggregative Impli-cations and Tests," American Economic Review, March 1963, pp. 55—84.

For an analysis of the economic implications of the national debt withinthis framework, see my recent paper, "Long_Run Implications of AlternativeFiscal Policies and the Burden of the National Debt," Economic Journal, De-cember 1961. The effect of nonreproducible tangible wealth and of the dis-crepancy between private net income and output will be examined in a forth-coming paper.

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SOME THEORIES OF INCOME DISTRIBUTIONNow it can be readily shown that this consumption function hasthe following basic implication: if fluctuates around an expo-nential growth trend with a stable rate of growth of, say, n percent per year, and if rt fluctuates similarly in the neighborhood ofa constant level r, then the ratio of wealth to income K/V willgravitate around a stable "equilibrium" value, say, a. This equi-librium value is related to the parameters of the consumption func-tion by the equation:

a= (1—c)/(n+b—rc) (6)

To prove this proposition, let us note that eq. (5) implies thesaving function = Vt — Ct = (1 — — (b — rc)Kt, i.e.,

saving is an increasing linear function of income and a decreasingfunction of the stock of wealth (since the model itself, as well asempirical verifications thereof, indicate that b > r and c < 1).But St is simply the rate of growth of wealth, or dK/dtMaking the substitution, dividing by rearranging terms, andusing eq. (6), we get:

(1 — c) — (b — rc) = n —

_________

1'g

(7)

From this equation, we can immediately infer that mustgravitate toward the value a given by eq. (6). For if K/Ye ex-ceeds this value, i.e., > aYt, then we see from eq. (7) that

will be smaller than n, the rate of growth of But thenmust be rising faster than and hence, must be de-

creasing in time and approaching a. Conversely, if at any pointfalls short of the equilibrium value, then the rate of accum-

ulation will become sufficiently brisk to cause to rise faster thanuntil equilibrium is re-established.

We can thus conclude that, if income exhibits an exponentialgrowth trend and r is stable in time, then the stability over timeof the ratio of wealth to income, or capital coefficient K/Y, canbe accounted for by the supply side of the capital markets, as animplication of the consumption function (5). In order to com-plete our explanation of the "constancies," we need to introducesome further hypothesis on the nature of technical progress andthe demand side of the capital markets, which insure an expo-

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SOME THEORIES OF INCOME DISTRIBUTIONnential growth trend and the stability of r. In particular, the fol-lowing two assumptions can be shown to be sufficient: (a) thattechnical progress, for the reasons mentioned by Scitovsky and re-lated mechanisms stressed by Fellner,8 tends on balance to beHarrod-neutral, thus satisfying equation (2); and (b) that tech-nical progress tends to shift the production function outward at aroughly constant proportional rate, or more precisely, that thetime path of the quantity H(t) of equation (2) tends to follow anexponential trend of the form

To show that assumptions (a) and (b), together with the con-sumption function (5), imply the three constancies, it is convenientto proceed in two steps. Let us suppose at first that the laborforce is constant and equal to E. Then = Eyt is proportionalto yt, and its growth is entirely due to rising output per capita,or productivity. Now assumption (a) (Harrod-neutral change)implies that, if the available capital is proportional to income, i.e.,K/Y is constant, then the rate of return r needed to clear thecapital markets will tend to remain constant; and the consumptionfunction insures that, with a constant r, the capital-output ratiowill be constant, provided Y grows exponentially. To completethe argument, it is therefore sufficient to show that if the capital-output ratio is constant, i.e.,

K=aYork—ay (8)

then assumption (b) insures that income will in fact follow an ex-ponential growth trend. To verify this last conclusion, we onlyneed to substitute eq. (8) into eq. (3), obtaining

y = H(t)fo[ay/H(t)].The value of y satisfying this equation, say, yt, can be written inthe form

yt = yoH(t) = yoH(O)9t

where Yo is a constant satisfying the condition = fo (ayo). Thusy, and hence Y, will tend to grow at the rate p, and hence alsoeq. (8) will hold, with the constant a given by eq. (6), after set-tingn=p.

This result can be illustrated in terms of Figure 1. lATe canthink of yo as the y coordinate of the point q at the intersection of

8See, e.g., William Feilner, Trends and Cycles in Economic Activity, NewYork, 1956, Chs. 7, 8, and 9.

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SOME THEORIES OF INCOME DISTRIBUTIONthe "initial" production function fo with the radius vector Oq,having equation k = ay. Then yt is represented by points at theintersection of this radius vector with a succession of outwardshifting production functions ft. These successive points of in-tersection are moving outward on the radius vector at the expo-nential rate p.

The reasoning is essentially unchanged if we drop the assump-tion that population is constant and assume instead that the laborforce is itself growing at the exponential rate p'—that is, E =EoeP't. The only difference is that now total income, =

= yoePtEoeP't = will grow at the rate p + p"and hence, the equilibrium value of the capital coefficient a willbe given by eq. (6) with n = p + p'.

We have thus shown that the three constancies can be explainedby the M — B consumption function, plus the hypothesis that tech-nical progress has tended, on balance, to be of the Harrod-neutralvariety and to take place at a roughly exponential rate. One sig-nificant implication of this model is that the rate of growth of in-come is completely determined by the rate of technical progress pand the rate of population growth p'—although it reflects in partalso the growth of capital per employee, which is brought about bythe consumption function, and occurs at the same rate as thegrowth in productivity.9 Hence, the growth trend of incomeis independent of the marginal propensity to consume c or, forthat matter, of the saving ratio S/Y; these quantities determineonly the equilibrium capital output ratio and hence the ray onwhich we move, but not the speed of movement.

Unfortunately, it is not possible to expatiate here on this impli-cation of the model, nor to bring out other interesting propertiesand possible generalizations, including the adaptability of the model

In other words, the growth p in per capita output is due only partly to theoutward shift in the production function, the remaining part being due to thegrowth of k, or in capital per man. It is this increase in capital per man whichenables output to grow along the ray Oq of Figure 1. If instead k were toremain constant, we would not be moving along the ray Oq, but instead along avertical line through q, and the growth of output would be smaller, and mightnot even be exponential. To illustrate, if the production function were ofthe Cobb-Douglas type (4), we would have Yt or yt =

Hence, if k were constant and H(t) = H(O)ePt, the rate of growthof would be only p(1 — a). We might also note that the constancy of thethree ratios requires only the constancy of the over-all rate of growth of incomen; we can therefore relax the assumption that p and p' are individually constantas long as their sum is reasonably stable.

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SOME THEORIES OF INCOME DISTRIBUTIONto an explanation of cycles as well as long-run trends.1° There are,however, two brief concluding comments I should like to indulgein. First, the alternative model I have presented does riot implythat the historical constancies will necessarily be maintained in thefuture. I can see no strong ground for confidence that technicalprogress will forever remain Harrod-neutral on balance, or that itwill continue to occur at a roughly constant rate (or that the sumof p and p' will remain constant); and a change in any one of theseconditions will in turn tend to disturb the constancy of the capital-output ratio. However, partly on intuitive grounds and partly forreasons too complex to report here, I would be inclined to expectthat the (full-employment) rate of growth n and the capital-output ratio are likely to change at best very slowly. My secondremark is that whether or not I have persuaded the reader of theusefulness of the specific model reported here, I hope at least tohave made a convincing case for the central importance of themuch-neglected supply side of the capital market for an under-standing of the behavior of the capital-output and the capital-labor ratios, and more generally, of the phenomena associated withgrowth.

In summary, I have tried to bring to light some shortcomings ofthe macroeconomic theories reviewed by Scitovsky. I have alsopresented an alternative model in the hope of undermining hiscontention that "no satisfactory explanation [of the constancies}has been offered as yet by the upholders of the marginal produc-tivity theory." \Vhether or not I have been successful in this lastrespect is left for the reader to decide.

REPLY by Tibor ScitovskyLet me say first of all how pleased I am that my survey should

have called forth such interesting and constructive comments. Ifeel apologetic toward Modigliani for having missed his and Ando'svery relevant and interesting paper, especially because I quite

Some of these implications are spelled out in Ando and Modigliani, AmericanEconomic Review, May 1959, and in "Long-Run Implications of AlternativeFiscal Policies and the Burden of the National Debt," Economic Journal,December 1961. It should also be noted that the model can be generalized toallow for monopolistic and oligopolistic market structures, provided the ratio ofprice to (long-run) average cost remains reasonably constant in time.

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SOME THEORIES OF INCOME DISTRIBUTIONagree that the role of the supply side of capital needs and deservesto be more fully explored.

As to the critical comments on my survey, let me begin by de-fending myself against Denison's charge of my having been undulycritical of the marginal productivity theory. I am sorry if Ihave created that impression, because I fully agree that marginalproductivity is the basic building block for explaining both incomedistribution and many other things in economics; and my criti-cism was only aimed at too exclusive and too naive a relianceon it.

The other criticisms of both Denison and Modigliani have to dowith the tail end of my survey, concerned with Kaldor's contri-bution and that of Phelps Brown and Weber. I was impressedmore with their approach than with their arguments, and with thegeneral proposition that when economic forces tend to stabilizeeach of several interdependent variables, they mutually reinforceeach other. This seemed and still seems to me an idea worth ex-ploring further, especially in the area under discussion, where somuch remains yet to be explained. Denison's point that changesin tax rates and prices make it impossible for all the interdependentvariables stabilized by market forces to be stabilized simultaneouslyis perfectly correct; but instead of destroying the original argu-ment, it merely introduces a range of indeterminacy into it. Istand corrected by Modigliani's criticism of my understanding ofPhelps Brown and Weber's argument, but find unconvincing hisobjection to Kaldor's argument as a complete and even more as apartial explanation. Modigliani's main objection seems to be "theassumption that, even at full employment, the rate of investmentis completely determined by the investment demand"; and I shouldlike to remind him that all Kaldor does is to shift the limit, up towhich he assumes this, from full employment to what Joan Robin-son calls the inflation barrier.

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